
theorem
  for X be compact non empty TopSpace
  for F be Point of R_Normed_Algebra_of_ContinuousFunctions(X)
    holds 0 <= ||.F.||
proof
  let X be compact non empty TopSpace;
  let F be Point of R_Normed_Algebra_of_ContinuousFunctions(X);
  reconsider F1=F as Point of
    R_Normed_Algebra_of_BoundedFunctions the carrier of X by Lm1;
  ||.F.|| =||.F1.|| by FUNCT_1:49;
  hence thesis by C0SP1:27;
end;
